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CHAPTER (III) KINEMATICS OF FLUID FLOW

- 3.1 Types of Fluid Flow.
- 3.1.1 Real - or - Ideal fluid.
- 3.1.2 Laminar - or - Turbulent Flows.
- 3.1.3 Steady - or - Unsteady flows.
- 3.1.4 Uniform - or - Non-uniform Flows.
- 3.1.5 One, Two - or - Three Dimensional Flows.
- 3.1.6 Rational - or - Irrational Flows.
- 3.2 Circulation - or - Vorticity.
- 3.3 Stream Lines, Flow Field and Stream Tube.
- 3.4 Velocity and Acceleration in Flow Field.
- 3.5 Continuity Equation for One Dimensional

Steady Flow.

Fluid Flow Kinematics

- Fluid Kinematics deals with the motion of fluids

without considering the forces and moments which

create the motion.

We define field variables which are functions of

space and time Pressure field, Velocity field

Acceleration field,

Types of fluid Flow 1. Real and Ideal Flow

If the fluid is considered frictionless with zero

viscosity it is called ideal. In real fluids the

viscosity is considered and shear stresses occur

causing conversion of mechanical energy into

thermal energy

Ideal

Real

Friction 0 Ideal Flow ( µ 0) Energy loss 0

Friction o Real Flow ( µ ?0) Energy loss 0

2. Steady and Unsteady Flow

Steady flow occurs when conditions of a point in

a flow field dont change with respect to time (

v, p, H..changes w.r.t. time

steady

unsteady

- Steady Flow with respect to time
- Velocity is constant at certain position w.r.t.

time

- Unsteady Flow with respect to time
- Velocity changes at certain position
- w.r.t. time

3. Uniform and Non uniform Flow

Y

Y

x

x

Non- uniform Flow means velocity changes at

certain time in different positions ( depends on

dimension x or y or z(

Uniform Flow means that the velocity is

constant at certain time in different positions

(doesnt depend on any dimension x or y or z(

uniform

Non-uniform

y

4. One , Two and three Dimensional Flow

x

Two dimensional flow means that the flow

velocity is function of two coordinates V f(

X,Y or X,Z or Y,Z )

One dimensional flow means that the flow

velocity is function of one coordinate V f( X

or Y or Z )

Three dimensional flow means that the flow

velocity is function of there coordinates V

f( X,Y,Z)

4. One , Two and three Dimensional Flow (cont.)

- A flow field is best characterized by its

velocity distribution. - A flow is said to be one-, two-, or

three-dimensional if the flow velocity varies in

one, two, or three dimensions, respectively. - However, the variation of velocity in certain

directions can be small relative to the variation

in other directions and can be ignored.

The development of the velocity profile in a

circular pipe. V V(r, z) and thus the flow is

two-dimensional in the entrance region, and

becomes one-dimensional downstream when the

velocity profile fully develops and remains

unchanged in the flow direction, V V(r).

5. Laminar and Turbulent Flow

- In Laminar Flow
- Fluid flows in separate layers
- No mass mixing between fluid layers
- Friction mainly between fluid layers
- Reynolds Number (RN ) lt 2000
- Vmax. 2Vmean

- In Turbulent Flow
- No separate layers
- Continuous mass mixing
- Friction mainly between fluid and pipe walls
- Reynolds Number (RN ) gt 4000
- Vmax. 1.2 Vmean

Vmean

Vmean

Vmax

Vmax

5. Laminar and Turbulent Flow (cont.)

Rotational and irrotational flows

The rotation is the average value of rotation of

two lines in the flow. (i) If this

average 0 then there is no rotation and the

flow is called irrotational flow

6. Streamline

A Streamline is a curve that is everywhere

tangent to it at any instant represents the

instantaneous local velocity vector.

Stream line equation

Where u velocity component in -X- direction v

velocity component in-Y- direction w velocity

component in -Z- direction

z

w

V

x

u

v

y

velocity vector can written as

Where i, j, k are the unit vectors in ve x,

y, z directions

Acceleration Field

- From Newton's second law,
- The acceleration of the particle is the time

derivative of the particle's velocity. - However, particle velocity at a point is the same

as the fluid velocity,

Mathematically the total derivative equals the

sum of the partial derivatives

Convective component

Local component

Similarly

Airplane surface pressure contours, volume

streamlines, and surface streamlines

NASCAR surface pressure contours and streamlines

7. Streamtube

- Is a bundle of streamlines
- fluid within a streamtube remain constant
- and cannot cross the boundary of the

streamtube. - (mass in mass out)

Types of motion or deformation of fluid element

Linear translation

Rotational translation

Linear deformation

angular deformation

8- Rotational Flow Irrotational Flow The rate

of rotation can be expressed or equal to the

angular velocity vector( )

Note

The flow is side to be rotational if

The fluid elements are rotating in space (see

Fig. 4-44 )

The flow is side to be irrotational if

The fluid elements dont rotating in space (see

Fig. 4-44 )

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rotational flow

Irrotational flow

9- Vorticity ( ? )

Vorticity is a measure of rotation of a fluid

particale Vorticity is twice the angular velocity

of a fluid particle

10- Circulation ( ? )

The circulation ( ? ) is a measure of rotaion

and is defined as the line integral of the

tangential component of the velocity taken around

a closed curve in the flow field.

?

. cos ?

NOTE The flow is irrotational if ?0,

?0, ?0

For 2-D Cartesian Coordinates

Y

dy

dx

x

? ? . area

Conservation of Mass ( Continuity Equation )

( Mass can neither be created nor destroyed ) The

general equation of continuity for three

dimensional steady flow

z

dz

dx

x

dy

y

Net mass in x-direction -

Net mass in y-direction -

Net mass in z-direction -

S net mass mass storage rate

0

General equation fof 3-D , unsteady and

compressible fluid Special cases 1- For steady

compressible fluid 2- For incompressible fluid

( ? constant )

Note The above eqn. can be used for steady

unsteady for incompressible fluid

3- For 2-D